Topology and Dynamics of Transcriptome (Dys)Regulation

Area of Science:

• Mathematical Biology
• Computational Biology
• Bioinformatics

Background:

• RNA transcripts reflect gene expression health, and identifying disruptive sequences is crucial for disease treatment.
• A mathematical approach has been developed to define a
• healthy
• RNA sequence with at most four distinct nucleotides (nt≤4).

Purpose of the Study:

• To explore the mathematical properties of healthy RNA sequences and their connection to complex mathematical structures.
• To investigate the relationship between these mathematical structures and disease-related RNA sequences, specifically microRNAs (miRNAs).

Main Methods:

• Defining a
• healthy
• sequence group (fp) with properties related to free groups and aperiodic characteristics.
• Analyzing the character variety of a four-punctured sphere (S24) and its singularities, which relate to Painlevé VI Equation solutions.
• Examining the connection between decorated character varieties of Painlevé equations and character varieties derived from oncomir seeds.

Main Results:

• The mathematical group (fp) generated by healthy RNA sequences exhibits properties close to a free group of rank nt-1.
• Singularities in the character variety are linked to algebraic solutions of the Painlevé VI Equation.
• A direct relationship was established between Painlevé equation character varieties and those calculated from oncomir seeds.

Conclusions:

• The study establishes a novel mathematical framework for understanding RNA sequence health and its disruptions.
• The findings demonstrate a significant link between complex mathematical equations (Painlevé) and biological RNA sequences, particularly miRNAs.
• This research holds promise for applications in cancer research and the study of neurodegenerative diseases.